Posted by **matt** on Monday, December 11, 2006 at 6:55pm.

wooden balls are numbered 1-75. Five balls are drawn at random. What is the probability of drawing 5 consecutive numbers if no replacement occurs.?

The first ball has a 1/75 chance of being selected. The second ball can be from either above or below the first, so it has a 2/74 chance of being chosen. The same process of selection continues through the fifth ball.

To find the probability that

*all* of these events will occur, you need to

*multiply* the probability of the individual events.

With this information, you should be able to answer your own question.

I hope this helps. Thanks for asking.

I don't think that's right PsyDAG. What if the first ball is #1 -- there is no number below. Second, what if you picked balls in the following order; 5,3,1,2,4 would this be counted as a "success" as the numbers are, when rearranged, consecutive.

I think this is a combinatorial problem. The number of ways do draw 5 balls from a bag of 75 is 75-choose-5 or (75!)/((75-5)!*(5!)) where ! denotes factorial. This translates to (75*74*73*72*71)/(1*2*3*4*5) = 17259390. Now then, there are exactly 70 5-consecutive-balls combinations that could be drawn. (1,2,3,4,5), (2,3,4,5,6), ... (71,72,73,74,75). So, the probability is 70/17259390 = something very small

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